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3 LabVIEW Math Functions 1. Create a VI that converts an angle value in radians to degrees. Use the following values to test

your VI: 180° is equal to π radians. Then convert the following values:

a. π/2 = 1.5708

b. 3 π/2 = 4.7124

c. 2 π = 6.2832

SOLUTION

Front Panel

Block Diagram

Answers to questions:

a.

b.

c.

2. Create a VI that converts temperature values in °F to °C and K.

32

1.8

273.15

T FT C

T K T C

The following values can be used to test the VI: 32°F = 0°C = 273.15 K; -40°F = -40°C = -233.15 K.

Then convert the following values:

a. 212°F

b. 98.6°F

© 2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This publication is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.

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c. 350°F

d. 1400°F

SOLUTION

Front Panel

Block Diagram

Answers to questions:

a.

b.

c.

d.

3. Create a VI that converts temperature values in °C to °F. The following values can be used to test

the VI: 32°F = 0°C; -40°F = -40°C. Then convert the following values:

a. 100°C

b. 37°C

c. 85°C

d. 1200°C

© 2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This publication is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.

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SOLUTION

Front Panel

Block Diagram

Answers to questions:

a.

b.

c.

d.

4. Maintenance needs to get a ramp up to a height of 2 meters, and company regulations do not

allow a ramp to be used with an angle greater than 30°. Create a VI to determine the required

length of the ramp (pictured in Figure 3.1.)

30°

2 m

Figure 3.1. Determining required ramp length

© 2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This publication is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.

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SOLUTION

Front Panel

Block Diagram

5. Some neighbors just added a particularly ugly addition to their home. You have a suspicion that

the addition is not in compliance with the homeowners’ association limit of 32 feet to the

highest point on the home. To surreptitiously check it out, you wait until mid afternoon and take

a photo from the street. From the photo you determine that the home’s shadow is making an

angle of 40° from the ground. Then you step off the length of the shadow along the ground (37

steps). NOTE: Typo in text: 37 steps (in figure), not 32 steps.

Create a LabVIEW VI to determine if the neighbors are in compliance with the neighborhood

height requirement. A possible VI front panel is shown in Figure 3.2.

a. Assume your feet are exactly one foot in length and determine the height of the

addition.

b. How far off can the “length of foot” assumption be before the conclusion (in

compliance, or not in compliance) would change?

© 2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This publication is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.

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Figure 3.2. Front panel of a possible VI configuration

SOLUTION

Front Panel

Block Diagram

© 2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This publication is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.

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Answers to questions:

a. If your foot is 12 inches long, the house is in compliance at 31.05 ft (shown above).

b. Your foot must be at least

12.37 inches long to change the result.

6. Pneumatically controlled valves are operated by changing the air pressure applied to a

diaphragm. The pressure, acting on the area of the diaphragm, generates a force that attempts

to move the valve stem.

airF P A

That force is countered by a spring that pushes on the diaphragm in the other direction.

spring springF k x

where

kspring is the spring constant

x is the extension of the spring

Control valves typically use air pressures ranging between 3 psi (lbf/in2) and 15 psi. The change

in applied force because of the pressure change causes the valve stem to move approximately 1

inch.

Determine:

a. The force applied to a 10-inch diameter diaphragm by 3 psi air.

b. The force applied to a 10-inch diameter diaphragm by 15 psi air.

c. The change in applied force (ΔF) as the air pressure increases from 3 to 15 psi.

d. The spring constant required to cause the valve stem to move 1 inch in response to the

calculated change in force.

Note: The difference version of the spring equation may be helpful:

spring springF k x

© 2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This publication is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.

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SOLUTION

Front Panel

Block Diagram

7. When fluids have to be transported long distances, pipelines can be an efficient, safe, and

economical alternative to trucking. But, because of fluid friction, the pressure of the fluid falls

over distance, and pumping stations are required at intervals to re-pressurize the fluid.

The pressure drop between pumping stations can be predicted (if it is due to fluid friction only)

with the following equation:

© 2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This publication is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.

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21

2avg

LP f V

D

where

f is the Moody (or Darcy) friction factor (no units)

ρ is the fluid density (kg/m3)

L is the distance between pumping stations (m)

D is the pipe diameter (m)

Vavg is the average fluid velocity (m/s)

The friction factor depends in a complicated fashion on fluid, flow rate, and pipe surface

conditions. For this problem, assume that f = 0.008.

Create a VI similar to Figure 3.3 that will allow you to enter the required values, and then

calculate and display the pressure drop in Pa (Pa = 1 N/m2)) and bars (1 bar = 105 Pa). Test your

VI with these values:

f = 0.008

ρ = 800 kg/m3

L = 15,000 m

D = 0.2 m

Vavg = 1.5 m/s

ΔP = 5.4 bar

Figure 3.3. VI for estimating pipeline pressure drop

Then, answer the following questions:

a. What will the pressure drop increase to if the distance between piping stations is

increased to 20,000 m?

b. What is the maximum distance between pumping stations that will keep the pressure

drop from exceeding 5 bars?

© 2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This publication is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.

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c. To increase throughput, it has been proposed to increase the average fluid velocity to

2.2 m/s. What is the expected pressure drop at the higher flow rate? Assume L = 15,000

m.

d. What will happen to the expected pressure drop if a different fluid with a density of

1100 kg/m3 is transported in the pipeline? Assume Vavg = 1.5 m/s.

SOLUTION

Front Panel, shown in Figure 3.3

Block Diagram

Answers to questions:

a.

© 2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This publication is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.

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b.

c.

d.

8. Three resistances in parallel are subjected to the same voltage drop. Create a VI that will

calculate the current through each resistor. Ohm’s law will be used for each resistor:

V I R

© 2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This publication is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.

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R1

R2

R3

Vin Vout

Figure 3.4. Resistors in parallel

Test your VI with these values:

Vin = +10 V

Vout = -5 V

R1 = 100 ohms I1 = 0.15 amp

R2 = 200 ohms I2 = 0.075 amp

R3 = 400 ohms I3 = 0.1 amp

Figure 3.5. VI for finding current through resistors in parallel

Then, use your VI to solve for the currents through each resistor in this problem:

Vin = +12 V

Vout = 0 V

R1 = 2500 ohms

R2 = 1000 ohms

R3 = 1200 ohms

SOLUTION

Front Panel – shown in Figure 3.5

© 2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This publication is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.

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Block Diagram

Answer to question:

© 2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This publication is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.

Full file at http://AplusTestbank.eu/Solution-Manual-for-LabVIEW-for-Engineers-136094295